However, he said it was a step in the right direction following the Trump-Kim summit in Singapore.

“This is obviously a gesture of carrying forward what they agreed to in Singapore and we take it as such,” Mr Mattis told reporters.

“We also look at it as a first step of a restarted process. So we do want to explore additional efforts to bring others home.”

Despite soaring rhetoric about denuclearisation before the Singapore meeting, the summit ended with only a vague aspirational goal for a nuclear-free Korean Peninsula without describing when and how that would occur.

Subsequent talks between US Secretary of State Mike Pompeo and senior North Korean officials got off to a rocky start earlier this month, with the North accusing the Americans of making “unilateral and gangster-like” demands on denuclearisation.

United Nations Honour Guard members carry boxes believed to contain the remains of US servicemen killed during the Korean War during a return ceremony at Osan Air Base, in Pyeontaek, South Korea (Staff Sgt Quince Lanford/US Army via AP)

On Wednesday, Mr Pompeo said a great deal of work remains ahead of a North Korea denuclearisation deal, but he declined to provide any timeline.

Mr Trump, addressing reporters on the South Lawn, said Vice President Mike Pence would greet the families and the remains of the soldiers.

“We have many others coming, but I want to thank Chairman Kim in front of the media for fulfilling a promise that he made to me, and I’m sure that he will continue to fulfil that promise as they search and search and search,” he said.

“These incredible American heroes will soon lay at rest on sacred American soil.”

Mr Pence, the son of a Korean War combat veteran, said in a statement that he will participate in the ceremony when the remains arrive in the US.

United Nations Command said the remains will be flown to Hawaii immediately after a full honours ceremony in Seoul on Wednesday.

The remains of American troops are on their way home from North Korea. I hope this brings peace and comfort to the families whose loved ones never returned from the Korean War. We must continue the search until every service member is brought home.